Relatively large modulation signal constellations such as 16-, 32-, and 64-QAM (Quandrature Amplitude Modulation) have been adopted in many wireless communications standards, such as EDGE (Enhanced Data Rates for GSM Evolution), HSPA (High Speed Packet Access), LTE (Long Term Evolution), and WiMax (Worldwide Interoperability for Microwave Access). Multiple Input-Multiple Output (MIMO) schemes employed by those standards create even larger modulation constellations.
A large modulation constellation increases the complexity of a demodulator. For example, the complexity of MLSE (Maximum Likelihood Sequence Estimation) demodulation increases exponentially with the size of the modulation constellation. Less complex solutions are available, for example, DFSE (Decision-Feedback Sequence Estimation), DFE (Decision-Feedback Equalization), etc. These solutions attempt to strike a balance between accuracy and complexity. Other techniques useful for demodulating signals in MIMO scenarios include Multi-Stage Arbitration (MSA) and Iterative Tree Search (ITS).
Serial Localization with Indecision (SLI) is a demodulation technique that approximates an MLSE demodulator with reduced complexity. The basic idea of SLI is to demodulate in a series of simpler stages, where each non-final stage attempts to localize the search for the benefit of the following stage. In the first stage, the symbol constellation is broken down into four overlapping subsets, and each subset is represented by its centroid. The first stage selects a subset and outputs the corresponding centroid as an intermediate symbol estimate. The use of centroid results in a residual signal that forms the input to the following stage. In the next stage, the selected subset is further broken down into four overlapping subsets and the process is repeated until the final stage is reached. Each non-final stage makes a choice among the reduced subsets and outputs an intermediate symbol estimates. The intermediate symbol estimates from each stage are summed to obtain the final symbol estimates. Indecision arises from representing the modulation constellation as overlapping subsets. Indecision is beneficial in a multi-stage structure, because indecision discourages an irreversible bad decision in an early stage.
In a SLI receiver, the residual signals from each stage are generally modeled as Gaussian noise. This is so for the following reasons. First, a Gaussian noise model is already used to model the internal noise of the receiver and it is natural to extend that model to other noise sources, such as residual signals. Second, the Gaussian noise model is a worst case noise model, therefore, is robust. Third, the Gaussian noise model is a well-understood model, for which the optimal processing is relatively simple and the appropriate metric is the familiar Euclidean metric. Nevertheless, the Gaussian model is not an accurate match for the discrete residual signal, especially when the number of data samples is small.
Accordingly, there remains a need to develop modulation techniques that account for the discrete nature of the residual signals in order to improve the performance of SLI demodulators.